# Finding the Coordinates of the Midpoint of a Line Segment

In this worksheet, students find the coordinates of the midpoint of a line segment, given the coordinates of its endpoints.

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Use Coordinates in All Four Quadrants

Difficulty level:

### QUESTION 1 of 10

Given the coordinates of the endpoints of a line segment, we can easily find the coordinates of the midpoint of the line segment.

The x-coordinate of the midpoint will be the mean average of the x-coordinates of each endpoint.

The y-coordinate of the midpoint will be the mean average of the y-coordinates of each endpoint.

Example

Find the coordinates of the midpoint of the line segment whose endpoints are at (-4, -3) and (2, 4)

The average of -4 and 2 is (-4 + 2) ÷ 2 = -2 ÷ 2 = -1

The average of -3 and 4 is (-3 + 4) ÷ 2 = 1 ÷ 2 = ½

So the midpoint of the line segment with endpoints at (-4, -3) and (2, 4) is at (-1, ½)

This is shown in the diagram below.

State the coordinates of the midpoint of the line segment whose endpoints are at

(4, 0) and (2, 4)

(Don't forget the brackets!)

State the coordinates of the midpoint of the line segment whose endpoints are at

(3, 0) and (1, 4)

State the coordinates of the midpoint of the line segment whose endpoints are at

(-3, 2) and (1, 4)

State the coordinates of the midpoint of the line segment whose endpoints are at

(-3, 2) and (3, 2)

State the coordinates of the midpoint of the line segment whose endpoints are at

(-5, 3) and (4, -1)

(use decimals if you have to)

State the coordinates of the midpoint of the line segment whose endpoints are at

(6, 3) and (2, 6)

(use decimals if you have to)

State the coordinates of the midpoint of the line segment whose endpoints are at

(5, -3) and (2, 7)

(use decimals if you have to)

State the coordinates of the midpoint of the line segment whose endpoints are at

(-6, -3) and (-2, -6)

(use decimals if you have to)

State the coordinates of the midpoint of the line segment whose endpoints are at

(7, -6) and (12, 6)

(use decimals if you have to)

State the coordinates of the midpoint of the line segment whose endpoints are at

(3, 46) and (12, 6)

(use decimals if you have to)

• Question 1

State the coordinates of the midpoint of the line segment whose endpoints are at

(4, 0) and (2, 4)

(Don't forget the brackets!)

(3, 2)
(3,2)
EDDIE SAYS
The x-coordinate is ½(4 + 2)
The y-coordinate is ½(0 + 4)
• Question 2

State the coordinates of the midpoint of the line segment whose endpoints are at

(3, 0) and (1, 4)

(2, 2)
(2,2)
EDDIE SAYS
The x-coordinate is ½(3 + 1)
The y-coordinate is ½(0 + 4)
• Question 3

State the coordinates of the midpoint of the line segment whose endpoints are at

(-3, 2) and (1, 4)

(-1, 3)
(-1,3)
EDDIE SAYS
The x-coordinate is ½(-3 + 1)
The y-coordinate is ½(2 + 4)
• Question 4

State the coordinates of the midpoint of the line segment whose endpoints are at

(-3, 2) and (3, 2)

(0, 2)
(0,2)
EDDIE SAYS
The x-coordinate is ½(-3 + 3)
The y-coordinate is ½(2 + 2)
• Question 5

State the coordinates of the midpoint of the line segment whose endpoints are at

(-5, 3) and (4, -1)

(use decimals if you have to)

(-0.5, 1)
(-0.5,1)
EDDIE SAYS
The x-coordinate is ½(-5 + 4)
The y-coordinate is ½(3 + -1)
• Question 6

State the coordinates of the midpoint of the line segment whose endpoints are at

(6, 3) and (2, 6)

(use decimals if you have to)

(4, 4.5)
(4,4.5)
EDDIE SAYS
The x-coordinate is ½(6 + 2)
The y-coordinate is ½(3 + 6)
• Question 7

State the coordinates of the midpoint of the line segment whose endpoints are at

(5, -3) and (2, 7)

(use decimals if you have to)

(3.5,2)
(3.5, 2)
EDDIE SAYS
The x-coordinate is ½(5 + 2)
The y-coordinate is ½(-3 + 7)
• Question 8

State the coordinates of the midpoint of the line segment whose endpoints are at

(-6, -3) and (-2, -6)

(use decimals if you have to)

(-4, -4.5)
(-4,-4.5)
EDDIE SAYS
The x-coordinate is ½(-6 + -2)
The y-coordinate is ½(-3 + -6)
• Question 9

State the coordinates of the midpoint of the line segment whose endpoints are at

(7, -6) and (12, 6)

(use decimals if you have to)

(9.5, 0)
(9.5,0)
EDDIE SAYS
The x-coordinate is ½(7 + 12)
The y-coordinate is ½(-6 + 6)
• Question 10

State the coordinates of the midpoint of the line segment whose endpoints are at

(3, 46) and (12, 6)

(use decimals if you have to)

(7.5, 26)
(7.5,26)
EDDIE SAYS
The x-coordinate is ½(3 + 12)
The y-coordinate is ½(46 + 6)
---- OR ----

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